Meeting 1 (13.10.2025 by Keremcan Doğan): Introduction and motivation, Algebra and geometry correspondence, A little history of geometry and physics, Klein and Erlangen program, Noether theorem, Galilean and Poincare groups, Group representations, Wigner classification, Dirac equation
Meeting 2 (27.10.2025 by Bilal Bulduk): Quadratic vector spaces, Clifford algebras, Gamma matrices, Low dimensional examples, Z_2 grading, Exterior algebra, Clifford algebra chessboard, Bott periodicity, Orthogonal group and its Lie algebra (Jose Figueroa-O’Farrill lecture notes, Spin geometry Section 1.1, 1.3, 1.4, 3.1)
Meeting 3 (17.11.2025 by Oğuzhan Selçuk): Adjoint and twisted adjoint actions, Pin and spin groups, Exact sequences for Pin(V)-O(V) and Spin(V)-SO(V) and double covering, Group representations, Pin and spin representations (Jose Figueroa-O’Farrill lecture notes, Spin geometry Section 3.2, 3.3)
Meeting 4 (24.11.2025 by Oğuzhan Selçuk): Complexification of Clifford algebras, An example of pin and spin representations for 2-dimensional complexified Clifford algebra via Pauli matrices, Topological and smooth manifolds, Coordinate charts and transition maps, Fiber bundles, Transition maps and local trivializations, Vector bundle, Tangent bundle (Jose Figueroa-O’Farrill lecture notes, Spin geometry Section 4.1, 4.2.1, 4.2.2)